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Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving

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Summary

Algebraic reasoning can reduce biased decision-making on the bat-and-ball problem. Prompting students to use algebra improves accuracy and generalization, with math anxiety also impacting performance.

Keywords:
Algebraic reasoningCognitive Reflection TestDebiasingDecision-makingJudgmentMath anxietyReasoning

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Area of Science:

  • Cognitive Psychology
  • Decision Science
  • Educational Psychology

Background:

  • The bat-and-ball problem is a common tool for assessing cognitive reflection and decision-making biases.
  • University students frequently exhibit biased responses to this problem, indicating challenges in rational judgment.

Purpose of the Study:

  • To investigate if algebraic cueing can serve as a debiasing strategy for the bat-and-ball problem.
  • To determine if participants can generalize algebraic reasoning to novel problem instances.

Main Methods:

  • 197 participants completed variants of the bat-and-ball problem under different cueing conditions.
  • One group received algebraic cues, including solving isomorphic algebra equations.
  • Math anxiety levels were assessed and correlated with problem accuracy.

Main Results:

  • Participants prompted with algebraic reasoning showed significantly higher accuracy compared to controls.
  • The debiasing effect was strongest when participants solved corresponding algebra equations.
  • Participants generalized algebraic strategies to new problems, reducing bias without explicit cues.
  • Math anxiety negatively correlated with accuracy on the bat-and-ball problem.

Conclusions:

  • Algebraic reasoning is an effective debiasing strategy for bat-and-ball problem variants under specific conditions.
  • This study provides the first evidence linking math anxiety to performance on the Cognitive Reflection Test.
  • Findings suggest that teaching algebraic approaches can improve rational decision-making.